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A Càdlàg Rough Path Foundation for Robust Finance

Allan, Andrew L.; Liu, Chong; Prömel, David J.


Chong Liu

David J. Prömel


Using rough path theory, we provide a pathwise foundation for stochastic Itˆo integration, which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, we introduce the so-called Property (RIE) for c`adl`ag paths, which is shown to imply the existence of a c`adl`ag rough path and of quadratic variation in the sense of F¨ollmer. We prove that the corresponding rough integrals exist as limits of left-point Riemann sums along a suitable sequence of partitions. This allows one to treat integrands of non-gradient type, and gives access to the powerful stability estimates of rough path theory. Additionally, we verify that (path-dependent) functionally generated trading strategies and Cover’s universal portfolio are admissible integrands, and that Property (RIE) is satisfied by both (Young) semimartingales and typical price paths.


Allan, A. L., Liu, C., & Prömel, D. J. (in press). A Càdlàg Rough Path Foundation for Robust Finance. Finance and Stochastics,

Journal Article Type Article
Acceptance Date Apr 19, 2023
Deposit Date May 2, 2023
Journal Finance and Stochastics
Print ISSN 0949-2984
Electronic ISSN 1432-1122
Publisher Springer
Peer Reviewed Peer Reviewed
Publisher URL

This file is under embargo due to copyright reasons.

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